双调和抛物方程的加权Lp估计
Weighted Lp Estimates for the Bi-Harmonic Parabolic Equation
DOI: 10.12677/PM.2015.52007, PDF, HTML, XML,  被引量 下载: 2,597  浏览: 8,905  国家自然科学基金支持
作者: 于华翠：上海大学理学院，上海
关键词: 双调和抛物方程；加权；Lp估计；正则性估计；Bi-Harmonic Parabolic Equation； Weighted； Lp Estimates； Regularity Estimates
摘要: Schauder估计和LP估计是偏微分方程基本的正则性估计。本文我们主要研究双调和抛物方程的一类新的正则性估计——加权LP估计。
Abstract: Schauder estimates and LP estimates are the basic regularity estimates in the partial differential equations. In this paper we mainly study a new class of regularity estimates, weighted LP esti-mates for the bi-harmonic parabolic equation.
文章引用：于华翠. 双调和抛物方程的加权Lp估计[J]. 理论数学, 2015, 5(2): 46-53. http://dx.doi.org/10.12677/PM.2015.52007

参考文献

[1] Wang, L. (2003) A geometric approach to the Calderón-Zygmund estimates. Acta Mathematica Sinica (Engl. Ser.), 19, 381-396.
[2] Caffarelli, L. and Peral, I. (1998) On W1,p estimates for elliptic equations in divergence form. Commu-nications on Pure and Applied Mathematics, 51, 1-21.
[3] Byun, S. and Wang, L. (2004) Elliptic equations with BMO coefficients in Reifenberg domains. Communications on Pure and Applied Mathematics, 57, 1283-1310.
[4] Byun, S. and Wang, L. (2005) Lp estimates for parabolic equations in Reifenberg domains. Journal of Functional Analysis, 223, 44-85.
[5] Byun, S. and Wang, L. (2005) Parabolic equations in Reifenberg domains. Archive for Rational Mechanics and Analysis, 176, 271-301.
[6] Byun, S. andWang, L. (2007) Parabolic equations in Time Dependent Reifenberg domains. Advances in Mathematics, 212, 797-818.
[7] Byun, S. andWang, L. (2007) Quasilinear elliptic equations with BMO coefficients in Lipschitz domains. Transactions of the American Mathematical Society, 359, 5899-5913.
[8] Mengesha, T. and Phuc, N. (2011) Weighted and regularity estimates for nonlinear equations on Reifenberg flat domains. Journal of Differential Equations, 250, 2485-2507.
[9] Mengesha, T. and Phuc, N. (2012) Global estimates for quasilinear elliptic equations on Reifenberg flat domains. Archive for Rational Mechanics and Analysis, 203, 189-216.
[10] Byun, S., Palagachev, D. and Ryu, S. (2013) weighted W1,p estimates for solutions of non-linear parabolic equations over non-smooth domains. Bulletin of the London Mathematical Society, 45, 765-778.
[11] Yao, F.P. (2014) Weighted gradient estimates for the general elliptic p(x)-Laplacian equations. Journal of Mathematical Analysis and Applications, 415, 644-660.
[12] Yao, F.P. (2014) Weighted Lp estimates for the elliptic Schrödinger operator. Journal of Mathematical Analysis and Applications, 33, 1-13.
[13] 周民强 (2003) 调和分析讲义(实变方法). 北京大学出版社, 北京.
[14] Acerbi, E. and Mingione, G. (2007) Gradient estimates for a class of parabolic systems. Duke Mathematical Journal, 136, 285-320.
[15] Byun, S., Yao, F.P. and Zhou, S.L. (2008) Gradient estimates in Orlicz space for nonlinear elliptic equations. Journal of Functional Analysis, 255, 1851-1873.
[16] Byun, S. and Ryu, S. (2013) Global weighted estimates for the gradient of solutions to nonlinear el-liptic equations. Annales de l’Institut Henri Poincare (C) Non Linear Analysis, 30, 291-313.
[17] Wang, L.H., Yao, F.P., Zhou, S.L. and Jia, H.L. (2009) Optimal regularity for the poisson equation. Proceedings of the American Ma-thematical Society, 137, 2037-2047.
[18] Yao, F.P. and Zhou, S.L. (2008) Global Lp estimates for the parabolic equa-tion of the Bi-harmonic type. Journal of Partial Differential Equations, 21, 315-334.
[19] Evans, L. (1997) Partial differential equations. American Mathematical Society, Providence.
[20] 陈亚浙, 吴兰成 (1997) 二阶椭圆型方程与椭圆型方程组. 科学出版社, 北京.

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